et A = {m, 4, 2, 13}, B = {1, 2, 4, 13, -2} and C = {1,3,5,7,9} Find AUB. Find ANC. Find (AUC)NB.
et A = {m, 4, 2, 13}, B = {1, 2, 4, 13, -2} and C = {1,3,5,7,9} Find AUB. Find ANC. Find (AUC)NB.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![### Set Operations and Venn Diagrams
#### Problem Statement
Given the sets:
\[ A = \{ m, 4, 2, 13 \} \]
\[ B = \{ 1, 2, 4, 13, -2 \} \]
\[ C = \{ 1, 3, 5, 7, 9 \} \]
We need to find the following:
1. \( A \cup B \)
2. \( A \cap C \)
3. \( (A \cup C) \cap B \)
### 1. Finding \( A \cup B \) (Union of Sets \( A \) and \( B \))
The union of two sets \( A \) and \( B \) includes all elements from both sets, without duplication.
\[ A \cup B = \{ m, 4, 2, 13 \} \cup \{ 1, 2, 4, 13, -2 \} \]
Steps:
- List all unique elements from both sets.
- Combine the lists, removing any duplicates.
Result:
\[ A \cup B = \{ m, 4, 2, 13, 1, -2 \} \]
### 2. Finding \( A \cap C \) (Intersection of Sets \( A \) and \( C \))
The intersection of sets \( A \) and \( C \) includes only those elements that are present in both sets.
\[ A \cap C = \{ m, 4, 2, 13 \} \cap \{ 1, 3, 5, 7, 9 \} \]
Steps:
- List elements that appear in both sets.
Since there are no common elements between sets \( A \) and \( C \):
Result:
\[ A \cap C = \emptyset \] (or equivalently, \( \{ \} \))
### 3. Finding \( (A \cup C) \cap B \)
First, calculate \( A \cup C \):
\[ A \cup C = \{ m, 4, 2, 13 \} \cup \{ 1, 3, 5, 7, 9 \} \]
Result:
\[ A \cup C = \{ m, 4, 2, 13, 1,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffa06b614-497d-40f0-b077-f4b4fca47baf%2F078ed03e-ddaf-456d-b3e5-b9f9d2c75013%2Fghvys7d_processed.png&w=3840&q=75)
Transcribed Image Text:### Set Operations and Venn Diagrams
#### Problem Statement
Given the sets:
\[ A = \{ m, 4, 2, 13 \} \]
\[ B = \{ 1, 2, 4, 13, -2 \} \]
\[ C = \{ 1, 3, 5, 7, 9 \} \]
We need to find the following:
1. \( A \cup B \)
2. \( A \cap C \)
3. \( (A \cup C) \cap B \)
### 1. Finding \( A \cup B \) (Union of Sets \( A \) and \( B \))
The union of two sets \( A \) and \( B \) includes all elements from both sets, without duplication.
\[ A \cup B = \{ m, 4, 2, 13 \} \cup \{ 1, 2, 4, 13, -2 \} \]
Steps:
- List all unique elements from both sets.
- Combine the lists, removing any duplicates.
Result:
\[ A \cup B = \{ m, 4, 2, 13, 1, -2 \} \]
### 2. Finding \( A \cap C \) (Intersection of Sets \( A \) and \( C \))
The intersection of sets \( A \) and \( C \) includes only those elements that are present in both sets.
\[ A \cap C = \{ m, 4, 2, 13 \} \cap \{ 1, 3, 5, 7, 9 \} \]
Steps:
- List elements that appear in both sets.
Since there are no common elements between sets \( A \) and \( C \):
Result:
\[ A \cap C = \emptyset \] (or equivalently, \( \{ \} \))
### 3. Finding \( (A \cup C) \cap B \)
First, calculate \( A \cup C \):
\[ A \cup C = \{ m, 4, 2, 13 \} \cup \{ 1, 3, 5, 7, 9 \} \]
Result:
\[ A \cup C = \{ m, 4, 2, 13, 1,
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